Collective behaviors

Walker T, Sesko D and Wieman C 1990 Collective behavior of optically trapped neutral atoms Phys.Rev.Lett. 64 408-11... 

Pig. 1.8 Collective behavior of a four dimensional CA (after [chate92]). 

Reynolds Boids is a good example of decentralized order not because the boids behavior is a perfect replica of the flocking of birds that occurs in nature — although it is a close enough match that Reynold s model has attracted the attention of professional ornithologists — but that much of the boids collective behavior is entirely unanticipated, and cannot be easily derived from the rules defining what each individual bold does. 

Hierarchical Structure. In order to be better able to simulate the hierarchical nature of many real-world complex systems, in which agent behavior can itself be best described as being the result of the collective behavior of some swarm of constituent agents. Swarm is designed so that agents themselves can be swarms of other agents. Moreover, Swarm is designed around a time hierarchy, Thus, Swarm is both a nested hierarchy of swarms and a nested hierarchy of schedules. 

Despite its simple local rule base, EINSTein has an impressive repertoire of emergent collective behaviors forward advance, frontal attack, local clustering, penetration, retreat, attack posturing, containment, flanking maneuvers. Guerrilla-like assaults, among many others. 

The 1996 Nobel Prize in physics went to three researchers who studied liquid helium at a temperature of 0.002 K, discovering superfluid helium. A superfluid behaves completely unlike conventional liquids. Liquids normally are viscous because their molecules interact with one another to reduce fluid motion. Superfluid helium has zero viscosity, because all of its atoms move together like a single superatom. This collective behavior also causes superfluid liquid helium to conduct heat perfectly, so heating a sample at one particular spot results in an immediate and equal increase in temperature throughout the entire volume. A superfluid also flows extremely easily, so it can form a fountain, shown in the photo, in apparent defiance of gravity. 

In the past five years, it has been demonstrated that the QELS method is a versatile technique which can provide much information on interfacial molecular dynamics [3 9]. In this review, we intend to show interfacial behavior of molecules elucidated by the QELS method. In Section II, we present the principle and the experimental apparatus of the QELS along with the historical background. The dynamic collective behavior of molecules at liquid-liquid interfaces was first obtained by improving the time resolution of the QELS method. In Section III, we show the molecular collective behavior of surfactant molecules derived from the analysis of the time courses of capillary wave frequencies. Since the... 

As reviewed above, there have been many QELS studies on liquid surfaces. However, until a few years ago, reports were scarce on molecular dynamics at liquid-liquid interfaces which used time courses of capillary wave frequency. Molecular collective behavior at liquid-liquid interfaces from a QELS study was first reported by Zhang et al. in 1997 [5]. 

The molecular collective behavior of surfactant molecules has been analyzed using the time courses of capillary wave frequency after injection of surfactant aqueous solution onto the liquid-liquid interface [5,8]. Typical power spectra for capillary waves excited at the water-nitrobenzene interface are shown in Fig. 3 (a) without CTAB (cetyltrimethy-lammonium bromide) molecules, and (b) 10 s after the injection of CTAB solution to the water phase [5]. The peak appearing around 10-13 kHz represents the beat frequency, i.e., the capillary wave frequency. The peak of the capillary wave frequency shifts from 12.5 to 10.0kHz on the injection of CTAB solution. This is due to the decrease in interfacial tension caused by the increased number density of surfactant molecules at the interface. Time courses of capillary wave frequency after the injection of different CTAB concentrations into the aqueous phase are reproduced in Fig. 4. An anomalous temporary decrease in capillary wave frequency is observed when the CTAB solution beyond the CMC (critical micelle concentration) was injected. The capillary wave frequency decreases rapidly on injection, and after attaining its minimum value, it increases... 

The important point to note is that these laws govern the collective behavior of the network over and above the physical laws which govern the behavior of each individual network element. 

Miller, D.L. 1985. Introduction to Collective Behavior . Wadsworth, Belmont, CA. 

Smelser, N. 1962. Theory of Collective Behavior. Free Press, New York. 

There are two main kinds of actions we are concerned with in this book. They correspond to individual and collective behaviors of objects. 

A corollary is the question of how many individuals it takes to form a collectivity and to display the collective properties how many molecules of water to have a boiling point, how many atoms to form a metal, how many components to display a phase transition Or, how do boiling point, metallic properties, phase transition etc. depend on and vary with the number of components and the nature of their interac-tion(s) In principle any finite number of components leads to a collective behavior that is only an approximation, however dose it may well be, an asymptotic approach to the true value of a given property for an infinite number of units. 

This behavior differs completely from the discrete one-electron absorptions of low-nuclearity metal cluster molecules [17]. Instead, it resembles the 5d - 6s,6p interband transition of colloidal gold. This demonstrates clearly that the AU55 cluster has electronic energy levels which are closely spaced in a developing band structure, quite similar to colloidal gold. On the other hand, these electrons do not seem to show a collective behavior which would give rise to the plasma resonance. 

Kreibig et al. [68] have recently proposed three possible explanations for the lack of the plasma resonance in AU55. The first is that collective behavior doesn t occur, due to localization of the 6s electrons. This doesn t appear to be in agreement with the bulk of the experimental indications mentioned above, nor with that which will appear below in Sect. 5.4. 

When mixing two surfactants species in a SOW system, an equilibrium takes place between the oil and water phases and the interface for each species. Since the two species do not necessarily exhibit the same affinity for the interface and the oil and water bulk phases, the compositions of the surfactant mixtures at interface and in the phases might be different. For instance if a very hydrophilic species is mixed with a very lipophihc one, as often recommended in the old formulation literature, then the hydrophihc surfactant has a strong tendency to partition in water, whereas the lipophihc one would partition in the oil. In this case the surfactant mixture in water will contain a large majority of hydrophilic species, i.e., it will be very hydrophilic, whereas the oil phase will predominantly contain the hpophihc species, with the remaining adsorbing at interface. This situation in which each species actuates on its own, more or less independently of the other, has been called non-collective behavior. Since the surfactant mixture composition at interface is often the one that commands the actual property of the system, such as the interfacial tension or the stabihty of the emulsion, it is most important to know how to calculate or measure the characteristics of the mixture present at interface. Such methods will be discussed in the next section. 

If the experimental data indicate a linear relationship, such as Eq. 1, which will be considered as an ideal case, then it means that the mixing in the system produces exactly the same mixing at interface as in the whole system, and a so-called collective behavior of the surfactant species takes place. 

The collective behavior corresponds to the same mixture proportions in bulk phases as at interface, so that the mixture may be treated as a pseudocomponent. This implies the same partitioning for the different species [38]. 

These equations may be generalized to multicomponent systems with a linear mixing rule as in Eq. 1. It is worth remarking that the goodness of the fit tends to improve when the number of components of the mixture increases. For instance, the deviation shown in Fig. 5 (right) for the mixture of C9 and C15 ortho-xylene sulfonates, disappears if 20% of C12 ortho-xylene sulfonate is added. It is conjectured that the presence of intermediate species improves the collective behavior. 

The main problem in mixing ethoxylated nonionics is that they often contain extremely different surfactant species that are likely to behave non-collectively, much more than in the case of ionic surfactants. This problem will be addressed in the next section. Again it seems that the presence of intermediate species tends to favor a collective behavior. 

It may be conjectured that collective behavior implies that the surfactants that make up the mixture are not too different, the presence of an intermediate being a way to reduce the discrepancy. When the activity coefficient is calculated from non-ideal models it is often taken to be proportional to the difference in solubihty parameters [42,43], which in case of a binary is the difference (3i - if the system is multicomponent, then the dil -ference is - Sm) y which is often less, because the mean value exhibits an average lower deviation. In other terms, it means that for a ternary in which the third term is close to the average of the two first terms, then the introduction of the third component reduces the nonideahty because (5i - 53) + ( 2 - < (5i - 52) -... 

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